Question

Suppose that y=f(x) is an even function such that (2,−3) is a point on the graph of . Which of the following points belong to the graph of ?

a) (−3,−2)


b) (2,3)


c) (3,−2)


d) (−2,−3)


e) (−2,3)


f) None of the above

Answer 1

Explanation:

Since y=f(x) is an even function, we know that f(-x) = f(x). This means that the graph of y=f(x) is symmetric with respect to the y-axis.

Since (2,-3) is a point on the graph of y=f(x), we know that f(2) = -3. Therefore, the point (-2,-3) must also belong to the graph of y=f(x), since f(-2) = f(2) = -3.

Similarly, since the graph of y=f(x) is symmetric with respect to the y-axis, the point (-2,3) must also belong to the graph of y=f(x), since it has the same x-coordinate as (2,-3) and its y-coordinate is the opposite.

Therefore, the points (-2,-3) and (-2,3) belong to the graph of y=f(x).